Fig. 2: Gradient variance scaling for SU compound layers, observable in Lie algebra.
From: Characterizing barren plateaus in quantum ansätze with the adjoint representation
Dots are numerical results while dotted lines are analytical predictions using the equations in the text. Showing results for computational basis input states of Hamming weight 1 and n/2 and the uniform superposition state \({\left\vert+\right\rangle }^{\otimes n}\), for n number of qubits ranging from 2 to 18 in steps of 2. The measurement operator is \(-i{h}_{12}^{z}=({\sigma }_{1}^{z}-{\sigma }_{2}^{z})/4\). Accounting for the randomness of initialization, there is good agreement of numerical results with the predictions. The error bars are too small to plot. Additional information on the numerics is in the Supplementary Information.
